A ship sails to an island at the rate of $15$ $km/h$ and sails back to the starting point at $10$ $km/h$. Find the average sailing speed for the whole journey.
What I tried,
Let the distance be $x$ $km$
Speed from starting point to island $=15$ $km/h$
Speed from island to St point $=10$ $km/h$
Time taken in first case= $\frac{x}{15}$ $h$
Similarly time taken in second case=$\frac{x}{10}$ $h$
What to do next?
Best Answer
Let $d$ denote the one-way distance.
It took the ship $\frac{d}{15}$ hours to get to the island.
It took the ship $\frac{d}{10}$ hours to get back from the island.
The total distance was $2d$.
The total travel-time was $\frac{d}{15}+\frac{d}{10}=\frac{5d}{30}=\frac{d}{6}$.
Hence the average speed was $\frac{2d}{\frac{d}{6}}=12$ km per hour.